Gauged linear sigma model and pion-pion scattering

Abstract

A simple gauged linear sigma model with several parameters to take the symmetry breaking and the mass differences between the vector meson and the axial vector meson into account is considered here as a possibly useful template for the role of a light scalar in QCD as well as for (at a different scale) an effective Higgs sector for some recently proposed walking technicolor models. An analytic procedure is first developed for relating the Lagrangian parameters to four well established (in the QCD application) experimental inputs. One simple equation distinguishes three different cases:1. QCD with axial vector particle heavier than vector particle, 2. possible technicolor model with vector particle heavier than the axial vector one, 3. the unphysical QCD case where both the KSRF and Weinberg relations hold. The model is applied to the s-wave pion-pion scattering in QCD. Both the near threshold region and (with an assumed unitarization) theglobal region up to about 800 MeV are considered. It is noted that there is a little tension between the choice of bare sigma mass parameter for describing these two regions. If a reasonable globa fit is made, there is some loss of precision in the near threshold region.

19 pages, 9 figures

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Cited by in corpus (21)

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• Weak decays of heavy hadrons into dynamically generated resonances
• The Glueball in a Chiral Linear Sigma Model with Vector Mesons
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• Predictions for ${\eta }_c\to \eta {\pi }^{+}{\pi }^{-}$ producing $f_0(500)$, $f_0(980)$ and $a_0(980)$
• Revising the $f_1(1420)$ resonance
• The $a_0(980)$ and $\Lambda (1670)$ in the ${\Lambda }_c^{+}\to {\pi }^{+}\eta \Lambda$ decay
• $B^0$ and $B_s^0$ decays into $J/\psi$ plus a scalar or vector meson
• Chiral Nonet Mixing in pi pi Scattering
• $f_2(1810)$ as a triangle singularity
• The $K\bar{K}\pi$ decay of the $f_1(1285)$ and its nature as a $K^{\ast }\bar{K}-cc$ molecule
• Chiral Nonet Mixing in ${\eta }^{\prime }\to \eta \pi \pi$ Decay
• ${\bar{B}}^0$ decay into $D^0$ and $f_0(500)$, $f_0(980)$, $a_0(980)$, $\rho$ and ${\bar{B}}_s^0$ decay into $D^0$ and $\kappa (800)$, $K^{\ast 0}$
• Probing the substructure of $f_0(1370)$
• Proximity of $f_0(1500)$ and $f_0(1710)$ to the scalar glueball
• Generalized linear sigma model with two glueballs
• Chiral Nonet Mixing in $\pi K$ Scattering
• Role of the $f_1(1285)$ state in the $J/\psi \to \varphi \bar{K}{K}^{\ast }$ and $J/\psi \to \varphi f_1(1285)$ decays
• $\bar{K}$ induced formation of the $f_0(980)$ and $a_0(980)$ resonances on proton targets
• Chiral Nonet Mixing in $\pi \eta$ Scattering
• Mass Spectrum of Non-Charmed and Charmed Meson States in Extended Linear-Sigma Model